Abstract
A generalisation of existing mechanical models is proposed to account for the relation between wood macroscopic properties and fibre microstructure and chemical composition. It is applied to understanding of the origin of anisotropic maturation strains measured at the outermost surface of the xylem. Various assumptions are considered for boundary conditions of the fibre during the progressive maturation process and are applied to experimental data from the literature. Assumptions that the fibre is fully restrained in displacement, or fully unrestrained or unrestrained in the transverse direction only are all incompatible with observations. Indeed, within the tree, the fibre is restrained in the longitudinal and tangential directions, but unrestrained in the radial direction towards the bark. Mixed boundary conditions must be introduced to correctly simulate both longitudinal and tangential maturation strains. In the context of an analytical axisymmetric model, this is estimated by considering a parameter of partial release of tangential stress during maturation. Consistence with data and with finite element computation in the case of a square fibre confirmed that, because of the unrestrained radial condition, a large part of the tangential maturation stress is released in situ.
References
Alméras, T., Costes, E., Salles, J.C. (2004a) Identification of biomechanical factors involved in stem shape variability between apricot-tree varieties. Ann. Bot.93:1–14.10.1093/aob/mch054Search in Google Scholar PubMed PubMed Central
Alméras, T., Gril, J., Yamamoto, H. (2004b) Modelling anisotropic maturation strains in wood in relation with fibre boundary conditions, microstructure and maturation kinetics: mechanical formulation of the fibre model. http://www.lmgc.univ-montp2.fr/~jgril/hf/.10.1515/HF.2005.057Search in Google Scholar
Archer, R.R. (1987) On the origin of growth stresses in trees. Part 1. Micromechanics of the developing cambial cell wall. Wood Sci. Technol.21:139–154.10.1007/BF00376194Search in Google Scholar
Barber, N.F. (1968) A theoretical model of shrinking wood. Holzforschung22:97–103.10.1515/hfsg.1968.22.4.97Search in Google Scholar
Barber, N.F., Meylan, B.A. (1964) The anisotropic shrinkage of wood: a theoretical model. Holzforschung18:146–156.10.1515/hfsg.1964.18.5.146Search in Google Scholar
Castera, P., Morlier, V. (1991) Growth patterns and bending mechanics of branches. Trees5:232–238.10.1007/BF00227530Search in Google Scholar
Cave, I.D. (1972) Swelling of a fibre-reinforced composite in which the matrix is water-reactive. Wood Sci. Technol.6:157–161.10.1007/BF00350828Search in Google Scholar
Cousins, W.J. (1976) Elastic modulus of lignin as related to moisture content. Wood Sci. Technol.10:9–17.10.1007/BF00376380Search in Google Scholar
Fournier, M., Chanson, B., Thibaut, B., Guitard, D. (1991) Mechanics of standing trees: modelling a growing structure subjected to continuous and fluctuating loads. 2. Three-dimensional analysis of maturation stresses in a standard broad-leaved tree. Ann. For. Sci.48:527–546.Search in Google Scholar
Guitard, D., Masse, H., Yamamoto, H., Okuyama, T. (1999) Growth stress generation: a new mechanical model of the dimensional change of wood cells during maturation. J. Wood Sci.45:384–391.10.1007/BF01177910Search in Google Scholar
Harrington, J.J., Booker, R., Astley, R.J. (1998) Modelling the elastic properties of softwood. Part 1: the cell-wall lamellae. Holz Roh- Werkstoff56:37–41.10.1007/PL00002608Search in Google Scholar
Kojima, Y., Yamamoto, H. (2004a) The effect of microfibril angle on the longitudinal tensile creep behavior of wood. J. Wood Sci.50:301–306.10.1007/s10086-003-0565-3Search in Google Scholar
Kojima, Y., Yamamoto, H. (2004b) Properties of the cell wall constituents in relation to the longitudinal elasticity of wood. Part 2: origin of the moisture-dependency of the longitudinal elasticity of wood. Wood Sci. Technol.37:427–434.10.1007/s00226-003-0177-5Search in Google Scholar
Koponen, S., Torati, T., Kanerva, P. (1989) Modelling longitudinal elastic and shrinkage properties of wood. Wood Sci. Technol.23:55–63.10.1007/BF00350607Search in Google Scholar
Sakurada, I., Nukushima, Y., Ito, T. (1962) Experimental determination of the elastic modulus of crystalline regions in oriented polymers. J. Polymer. Sci.10.1002/pol.1962.1205716551Search in Google Scholar
Sassus, F., Alméras, T., Gril, J., Yamamoto, H. (2004) Modélisation des déformations de maturation de la fibre. Cah. Sci. Bois (in press).Search in Google Scholar
Terashima, N. (1990) A new mechanism for the formation of a structurally ordered protolignin macromolecule in the cell wall of tree xylem. J. Pulp Pap. Sci.16:150–155.Search in Google Scholar
Yamamoto, H. (1998) Generation mechanism of growth stresses in wood cell walls: roles of lignin deposition and cellulose microfibril during cell wall maturation. Wood Sci. Technol.32:171–182.10.1007/BF00704840Search in Google Scholar
Yamamoto, H. (1999) A model of the anisotropic swelling and shrinking process of wood. Part 1: generalisation of Barber's wood fibre model. Wood Sci. Technol.33:311–325.Search in Google Scholar
Yamamoto, H., Kojima, Y. (2002) Properties of the cell wall constituents in relation to the longitudinal elasticity of wood. Part 1: formulation of the longitudinal elasticity of an isolated wood fiber. Wood Sci. Technol.37:427–434.10.1007/s00226-001-0128-ySearch in Google Scholar
Yoshida, M., Okuyama, T. (2002) Techniques for measuring growth stress. Holzforschung56:461–467.10.1515/HF.2002.071Search in Google Scholar
© by Walter de Gruyter Berlin New York
